Assessment, monitoring and control of drilling operations and/or geological-characteristic assessment

ABSTRACT

In monitoring/control of drilling operation a dimensionality of a full-scale model (e.g., characterizing variables related to cuttings transport, gas migration and/or the like) is reduced and data from a plurality of geographically distributed (e.g., depth varying) sensors is received, and a surrogate model is used to estimate variables in real-time. Use of the surrogate model may enable, e.g., particle-filtering processes to be employed during the estimation while still allowing for real-time estimations, avoiding excessive use of reasonable computational resources (e.g., memory and processing speeds) and/or the like. Operating controls or the like may then be set based on the estimated variables. For example, drilling control parameters may be adjusted based on estimated variables to avoid lost circulation, kicks, stuck pipe, and catastrophic events, optimize drilling parameters such as rate of penetration, improve drilling success probabilities and efficiency and/or the like.

BACKGROUND

This disclosure relates in general to assessing drilling procedures and/or geological characteristics via processing of models, such as model reduction and/or use of surrogate models. Not by way of limitation, the disclosure describes, for example, assessments of geological characteristics pertaining, e.g., to oilfield-drilling operations, based on analysis of real-time data from a plurality of distributed sensors.

Having the capability to understand underground properties and characteristics is very valuable. For example, resources such as oil and natural gas are underground, and human populations are highly reliant on these resources. Nevertheless, successful extraction of resources depends on properly identifying extraction sites and effectively and dynamically tailoring extraction techniques to reach and extract the resources. For example, knowing properties (e.g., location and other properties) about a resource may improve an operator's choice of: a drill-site location, a drilling path (e.g., a non-vertical path), a drill speed, etc. Further, immediate identification of events may allow an operator to quickly respond to the event and avoid catastrophic and/or very costly aftermaths. However, given the many variables affecting geophysical responses to extraction efforts, estimating geophysical properties is itself a difficult task—much less estimating changing properties in real-time.

BRIEF SUMMARY

Equations or models may be used to estimate variables characterizing real-world properties, such as variables related to oilfield drilling or geophysics. The equations or models may include, e.g., partial differential equations or discretized partial differential equations (e.g., discretized using techniques such as finite volume, finite differences and/or finite element techniques) that result in full models. However, dynamically solving for variables using the full models may be difficult or impossible given a large number of unknown variables. Even estimation techniques may be impractical and/or extremely computationally expensive for real-time applications due to a requisite number of iterations (e.g., when using a Monte Carlo technique).

In one embodiment of the present invention, a dimensionality of a full-scale model (e.g., characterizing variables related to cuttings transport, gas migration and/or the like) is reduced, in an embodiment, data from a plurality of geographically distributed (e.g., depth varying) sensors is received, and a surrogate model is used to estimate variables in real-time. Use of the surrogate model may enable, e.g., particle-filtering processes to be employed during the estimation while still allowing for real-time estimations, avoiding excessive use of reasonable computational resources (e.g., memory and processing speeds) and/or the like. Operating controls or the like may then be set based on the estimated variables. For example, drilling control parameters may be adjusted based on estimated variables to avoid lost circulation, kicks, stuck pipe, and catastrophic events, optimize drilling parameters such as rate of penetration, improve drilling success probabilities and efficiency and/or the like.

Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating various embodiments, are intended for purposes of illustration only and are not intended to necessarily limit the scope of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is described in conjunction with the appended figures:

FIG. 1 illustrates an embodiment of a drilling system including a plurality of sensors that transmit data along a wired drill string;

FIG. 2 depicts a block diagram of an embodiment of a geophysical-characteristic estimator system;

FIG. 3 illustrates a flowchart of an embodiment of a process for estimating a geophysical characteristic;

FIG. 4 depicts a block diagram of an embodiment of a geophysical-model generator system;

FIG. 5 illustrates a flowchart of an embodiment of a process for generating geophysical models;

FIG. 6 depicts a block diagram of an embodiment of a model-modification system;

FIG. 7 illustrates a flowchart of an embodiment of a process for modifying models;

FIGS. 8 a-8 b each depict a block diagram of an embodiment of a system for estimating a geophysical characteristic;

FIGS. 9 a-9 c each illustrate a flowchart of an embodiment of a process for estimating a geophysical characteristic;

FIG. 10 depicts a block diagram of an embodiment of a computer system;

FIG. 11 depicts a block diagram of an embodiment of a special-purpose computer;

FIG. 12 shows error norms for cutting volume and pressure resulting from models, in accordance with an example;

FIG. 13 shows cuttings volume along the annulus at an instance in time obtained from models, in accordance with an example;

FIG. 14 shows time-varying estimates of pressure, cuttings volume and cuttings slip velocity along an annulus, by incorporating a model in a particle filtering framework, in accordance with an example;

FIG. 15 shows representations of mean error and standard deviations of estimations from ‘true’ quantities, in accordance with an example; and

FIG. 16 illustrates an example of a particle-filtering framework with switching models.

In the appended figures, similar components and/or features may have the same reference label. Further, various components of the same type may be distinguished by following the reference label by a dash and a second label that distinguishes among the similar components. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.

In the appended figures, similar components and/or features may have the same reference label. Where the reference label is used in the specification, the description is applicable to any one of the similar components having the same reference label.

DETAILED DESCRIPTION

The ensuing description provides preferred exemplary embodiment(s) only, and is not intended to limit the scope, applicability or configuration of the invention. Rather, the ensuing description of the preferred exemplary embodiment(s) will provide those skilled in the art with an enabling description for implementing a preferred exemplary embodiment of the invention. It being understood that various changes may be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the appended claims.

Embodiments of the invention may use sensor readings for model parameter estimation. In embodiments of the present invention, the models may be models built using data from the sensors and model reduction techniques, such as model reduction based on Lowener matrices. In an embodiment of the present invention, dimensionality of a model, may be reduced using a model reduction technique such that the model may be used to estimate values for (e.g., drilling-related) variables of interest in real-time based on current sensor readings. The sensor readings may include data collected by one or more sensors. In some instances, the data is collected by one or more sensors positioned at multiple locations (e.g., multiple depths and/or geographic coordinates). A single sensor may collect multiple-location data (e.g., based on movement of the sensor), and/or multiple sensors distributed geographically with respect to each other (e.g., at different depths and/or geographic coordinates) may be used to collect the multiple-location data. Thus, in some instances, the multiple-location data comprises geographically distributed and simultaneously collected data.

Sensor data may be collected while or after a drilling process is occurring. In some instances, sensors are coupled to or part of a wellbore instrument or a “string” of such instruments in a wellbore using a wired pipe string for conveyance and signal communication. The wired pipe string may be assembled and disassembled in segments to effect conveyance in a manner known in the art for conveyance of segmented pipe through a wellbore. While the present invention is described as used with tools commonly conveyed on a wireline (“wireline tools”), the invention may be implemented with any other type of downhole tool like logging-while-drilling “LWD” tools. In effect, embodiments of the present invention may used with wireline tools/sensors, LWD tools/sensors, wired drill pipe, coiled tubing and/or the like.

Referring first to FIG. 1, an illustration of an embodiment of a drilling system 100 including a plurality of sensors that transmit data along a wired drillstring is shown. A drilling rig 24 or similar lifting device moves a wired drill pipe 20 within a wellbore 18 that has been drilled through subsurface rock formations, shown generally at 11. The wired drill pipe 20 may be extended into the wellbore 18 by threadedly coupling together end-to-end a number of segments (“joints”) 22 of wired pipe or tubing. Wired pipe may be structurally similar to ordinary drill pipe (see, e.g., U.S. Pat. No. 6,174,001, which is hereby incorporated by reference in its entirety) and includes a cable associated with each pipe joint that serves as a signal communication channel. The cable may be any type of cable capable of transmitting data and/or signals, such as an electrically conductive wire, a coaxial cable, an optical fiber or the like. Wired pipe typically includes some form of signal coupling to communicate signals between adjacent pipe joints when the pipe joints are coupled end to end as shown in FIG. 1. For example, U.S. Pat. No. 6,641,434, which is hereby incorporated by reference in its entirety, provides a non-limiting example of a type of wired drill pipe having inductive couplers at adjacent pipe joints that may be used with the present invention. However, the present invention should not be limited to the wired drill pipe 20 and can include other communication or telemetry systems, including a combination of telemetry systems, such as a combination of wired drill pipe, mud pulse telemetry, electronic pulse telemetry, acoustic telemetry or the like.

Several of the components disposed proximate the drilling unit 24 may be used to operate components of the system. These components will be explained with respect to their uses in drilling the wellbore to better enable understanding the invention. The wired drill pipe 20 may be used to turn and axially urge a drill bit into the bottom of the wellbore 18 to increase its length (depth). During drilling of the wellbore 18, a pump 32 lifts drilling fluid (“mud”) 30 from a tank 28 or pit and discharges the mud 30 under pressure through a standpipe 34 and flexible conduit 35 or hose, through the top drive 26 and into an interior passage (not shown separately in FIG. 1) inside the wired drill pipe 20. The mud 30 exits the wired drill pipe 20 through courses or nozzles (not shown separately) in the drill bit, where it then cools and lubricates the drill bit and lifts drill cuttings generated by the drill bit to the Earth's surface.

When the wellbore 18 has been drilled to a selected (or predetermined) depth, the wired drill pipe 20 may be withdrawn from the wellbore 18. An adapter sub 12 and a well logging instrument 13 may then be coupled to the end of the wired drill pipe 20, if not previously installed. The wired drill pipe 20 may then be reinserted into the wellbore 18 so that the well logging instrument 13 may be moved through, for example, a highly inclined portion 18A of the wellbore 18, which would be inaccessible using armored electrical cable (“wireline”) to move the instruments 24. The well logging instrument 13 may be positioned on the wired drill pipe 20 in other manners, such as by pumping the well logging instrument 13 down the wired drill pipe 20 or otherwise moving the well logging instrument 13 down the wired drill pipe 20 while the wired drill pipe 20 is within the wellbore 18.

During well logging operations, the pump 32 may be operated to provide fluid flow to operate one or more turbines (not shown in FIG. 1) in the well logging instrument 13 to provide power to operate certain devices in the well logging instrument 13. Power may be provided to the well logging instrument 13 in other ways as well. For example, the turbine(s) may be used to provide power to the recharge batteries located either in a special power sub or in each individual instrument or tool. In other examples, the wired drill pipe 20 may be rotated to provide power to the well logging instrument 13. In still other examples, batteries may be used to operate the well logging instrument 13. In a non-preferred embodiment, power may be transmitted downhole through the wired drill pipe 20, and, in such an embodiment, may be amplified or used to power or recharge a battery in the special power sub to provide power to the instruments. The foregoing examples of power provision may be used individually or in any combination. Other manners of powering the well logging instrument 13 may be used as appreciated by those having ordinary skill in the art.

The wired drill pipe 20 (and/or a well-logging instrument 13) may include one or more sensors (e.g., an assembly or a “string” of sensors), which may be, e.g., located along the wired drill pipe 20 or coupled to a lower end of the wired string. The sensors may include one or more wireline configurable well logging instruments and/or one or more LWD instruments. As used in the present description, the term “wireline configurable well logging instruments” or a string of such instruments means one or more well logging instruments that are capable of being conveyed through a wellbore using armored electrical cable (“wireline”). Wireline configurable well logging instruments are thus distinguishable from LWD instruments, which are configurable to be used during drilling operations and form part of the pipe string itself. While generally referred to as the well logging instrument 13, the well logging instrument 13 may consist of one, an assembly, or a string of wireline configurable logging instruments.

The sensors may detect signals e.g., before the well logging instrument 13 is moved along the wellbore (e.g., while the wellbore is being drilled), as the well logging instrument 13 and/or wired drill pipe 20 are moved along the wellbore by moving the wired drill pipe 20 as explained above, and/or after the well logging instrument 13 and/or wired drill pipe 20 have been moved to one or more destination locations. FIG. 1 illustrates a non-limiting example of a well logging instrument 13 with an induction resistivity instrument 16, a gamma ray sensor 14 and a formation fluid sample taking device 10 (which may include a fluid pressure sensor (not shown separately)). Thus, in this embodiment, multiple types of sensors are provided. Examples of other types of sensors include, without limitation, density sensors, neutron porosity sensors, acoustic travel time or velocity sensors, seismic sensors, accelerometers, neutron induced gamma spectroscopy sensors and microresistivity (imaging) sensors.

In some instances, a wired drill pipe 20 (and/or wired string) and/or well logging instrument 13 may include one or more types of sensors. There may be a plurality of sensors of a given type. For example, a wired drill pipe 20 and/or well logging instrument 13 may include a plurality of pressure-sensitive sensors (e.g., a fluid pressure sensor). A number of sensors of one type may or may not be the same as a number of sensors of another type. A sensor of one type may or may not be co-located with a sensor of another type. In some instances, sensors of a given type may be located substantially regularly along the wired pipe string. A sensor may be partially or fully enclosed within a housing. The housing may include one or more inlets and/or one or more exposed areas, such that the sensor may be exposed to the surrounding environment (e.g., to liquids, gases, cuttings, etc.).

Sensors may be located at different geophysical positions with respect to each other. In some instances, two, more or all sensors are located at depth relative to a ground level. A separation between a depth of at least two sensors and/or an average depth separation between adjacent sensors (generally, or sensors of a same or similar type) may be, e.g., greater than about 10, 25, 50, 100, 250, 500, or 1,000 feet. In some instances, an average separation between adjacent sensors of a same type is at least about 100-200 feet. In some instances, the sensors span a depth distance of at least about 50, 100, 250, 500, 1,000, 2,000, or 5,000 feet. In one instance, the sensors span a depth distance that is at least about 500 feet and less than about 1,000 feet. In some instances, two, three or more of the sensors may be located within different geological formation layers.

The sensors may be configured to regularly or continuously collect measurements and/or to collect measurements upon an instruction. In one instance, one, more or all sensors collect at least one measurement every 1 second, 5 seconds, 15 seconds, 30 seconds, 1 minute, 3 minutes, 5 minutes, 10 minutes, 30 minutes, 1 hour, 2 hours or 4 hours. Collected data may have a sampling rate of, e.g., about 0.1 mHz to 1 GHz depending on acquisition capabilities. For example, the sampling rate can be at least about 10 Hz, 1 Hz, 0.5 Hz, 0.1 Hz, 50 mHz, 25 mHz, 10 mHz, 1 mHz, 0.5 mHz, or 0.25 mHz.

The transmitter at the surface may comprise, e.g., a telemetry transmitter/receiver 36A, which may be used to wirelessly transmit signals from the wired drill pipe 20 to a transmitter/receiver 36B. Thus, the wired drill pipe 20 may be freely moved, assembled, disassembled and rotated without the need to make or break a wired electrical or optical signal connection. Signals from the receiver 36B, which may be electrical and/or optical signals, for example, may be transmitted (such as by wire, cable or wirelessly) to a recording unit 38 for decoding and interpretation. The decoded signals may correspond to the measurements made by one or more of the sensors (e.g., sensors in the well logging instruments 10, 14, 16). In some embodiments, the signal or commands can be transmitted from the surface recording unit 38 via 36B and 36A to the well logging instrument 13. The recording unit 38 may comprise a processor for processing data as well as other components to receive, manipulate and convert data. Signals from the sensors may be transmitted from the sensor via the wired drill pipe 20 (and the well logging instrument 13 in some instances) to a transmitter at the surface.

The functions performed by the adapter sub 12 may include providing a mechanical coupling (explained below) between the lowermost threaded connection on the wired drill pipe 20 and an uppermost connection on the well logging instrument 13. The adapter sub 12 may also include one or more devices (explained below) for producing electrical and/or hydraulic power to operate various parts of the well logging instrument 13. The adapter sub 12 also includes the communication adapter circuit to allow the communication between the wired drill pipe and the well logging instrument 13. Finally, the adapter sub may include signal processing and recording devices (explained below) for selecting signals from the well logging instrument 13 for transmission to the surface using the wired drill pipe 20 and recording signals in a suitable storage or recording device (explained below) in the adapter sub 12.

It will be appreciated by those skilled in the art that in other examples the top drive 26 may be substituted by a swivel, kelly, kelly bushing and rotary table (none shown in FIG. 1) for rotating the wired drill pipe 20 while providing a pressure sealed passage through the wired drill pipe 20 for the mud 30. Accordingly, the invention is not limited in scope to use with top drive drilling systems.

Using drill pipe as a drill pipe carrier for the well logging instrument 13 may protect sensors as they are moved underground. In some instances, a sensor (e.g., of the well logging instrument) may be initially latched or otherwise secured inside a drill pipe carrier at a retracted position, such that the sensor is completely or at least substantially encased by the drill pipe carrier and not in contact with the casing or formation. When the tool's functions are required, the sensor or a component coupled to the sensor may be disengaged such that it may be exposed to the surrounding geophysical environment. For example, well logging instrument 13 may be disengaged and move away from a top of the drill pipe carrier to an extended position and maintain communication with the wired drill pipe 20. As another example, sensors may be surrounded by an outer housing. Exposed surfaces of sensors may be initially covered by a outer housing. The sensors and/or outer housing may then be moved, such that the exposed surfaces of the sensors are then exposed through cavities in the outer housing. For example, a tube comprising a plurality of holes may surround a plurality of sensors and may be movable relative to the sensors, such the holes may move from aligning with the sensors to not aligning with the sensors.

Electrical signals, such as command signals, may be transmitted from Earth's surface (e.g. surface of the wellsite) to control the well logging instrument 13, the drill pipe carrier and/or components regulating whether sensors are exposed to surrounding environments. For example, a command may be transmitted along the wired pipes to move the well logging instrument to the extended position, the retracted position, or another position. The signals may also be transmitted from the adapter sub 12. For example, the adapter sub 12 may contain processing to determine if the well logging instrument 13 is properly positioned and should be retracted to begin obtaining measurements of the wellbore and/or formation surrounding the wellbore. The adapter sub 12 may receive control signals form a component at the surface of the wellsite, such as a processor, surface control unit, or other component. The control signals may be transmitted directly from the recording unit 38 or other component, such as a surface control unit or a processor at the surface of the wellsite, to the well logging instrument 13 and/or the drill pipe carrier 100. As another example, a command may be transmitted along the wired pipes to move sensors to an exposed position, a non-exposed position or another position. Thus, sensors may be exposed to the formation during select time periods. The drill pipe carrier and/or wired drill pipe 20 may optionally include electronics for transmitting and receiving signals related to the movement of a sensor, a sensor component (e.g., the well logging instrument) or an outer housing component affecting sensor exposure. Additional details about sensors, couplers, and well logging instruments may be found, e.g., in U.S. application Ser. No. 12/728,894, which is hereby incorporated by reference in its entirety.

Referring next to FIG. 2, a block diagram of an embodiment of a geophysical-characteristic estimator system 200 is shown. The system 200 includes a database 205 of stored full-scale models. The full-scale models may include, e.g., geophysical models. The full-scale models may model and/or estimate variables representing properties related to underground features and/or resources. The full-scale models may relate to earth-contained resources, such as oil and/or natural gas and/or to extraction properties related to these resources. The full-scale models may relate to propagation properties of solids (e.g., cuttings), fluids and/or gases generally or in relation to particular fluids and/or gases (e.g., oil or natural gas) in pure or unpure form. The full-scale models may relate to earth formations, such as depths, densities and/or porosities of layers (e.g., rock or shale layers). The full-scale models may include variables, such as one or more fluid flow rates (e.g., drilling fluid flow rate), one or more fluid densities (e.g., drilling fluid density), one or more shapes of one or more objects (e.g., shapes of cuttings), one or more sizes of one or more objects (e.g., sizes of cuttings), one or more surrounding-environment sizes (e.g., dimensions of drilling pipes and/or annulus walls), one or more interactions (e.g., cuttings' interactions with drilling pipe and annulus walls), one or more volumes or concentrations (e.g., volumes of cuttings along an annulus), one or more velocities (e.g., velocity of cuttings), and/or one or more environment dependencies (e.g., volume of cuttings for a given pressure and/or temperature).

The models may or may not be comprehensive with regard to a variable of interest. For example, a first model may relate to a predicted speed at which a fluid travels and a second model may relate to a predicted location at which a high concentration of a fluid resource may be found, or a single model may combine these predictions. The models may include one or more non-linear components and/or a large number (e.g., more than 5, 10, 20, 50, 100, 250, 500, 1,000, 2,500 or 5,000) of non-fixed and/or unknown variables. The models may include one or more hidden variables (e.g., variables not practically measurable).

The models may be time-evolving models and/or may include a time-evolving feature. The models may involve one or more differential equations. It may be difficult or impractical to solve the models and solving and/or approximating a solution of the models may be computationally expensive or prohibitive (e.g., with regard to processing and/or memory capabilities). Control based on process models may require solutions to, e.g., large Lyapunov and Sylvester equations. The models may require application of a simulation-based and/or multiple-iteration estimation technique. The models may rely on a recursive technique, Bayesian-inference technique and/or Monte-Carlo technique to estimate variables. In some instances, particle-filtering, Kalman-filtering and/or Ensemble Kalman-filtering techniques are used to estimate variables (e.g., when linearity conditions and additive Gaussian noise presence are assumed). The database may include one or models—each of which may or may not be alternative models related to similar or the same parameters. For example, multiple models may relate to a prediction of a drill-fluid rate—each including different parameters or different expected inputs.

The models may include models related to processes involved in oilfield drilling applications. The models may include models of, e.g., movement of liquids (e.g., drilling fluid), solids (e.g., cuttings) and gas along an annulus (e.g., a void between a drill string and a formation being drilled); a steering tendency of a bottom hole assembly (BHA) (which may include, e.g., a drill bit, drill collars, and drilling stabilizers), and/or vibrations of a drill string. In some instances, models relate to estimates of cuttings transport, gas migration and/o predictions and assessment of rare events (e.g., lost circulation, catastrophic failure, sensor failure, etc.). The models may include one or more unknown parameters and/or initial states. The unknown parameters and state characterizations may or may not have known real-world significance. For example, it may be known that a flow of a drilling fluid is affected by a friction of liquid resources and a concentration of cuttings underground. Other examples of influencing variables include: a geometry of a BHA, a wellbore geometry, a temperature, a density of a drilling fluid, etc. In some instances, it may be difficult or impossible to measure these influencing variables.

An offline surrogate geophysical model generator 210 may modify one or more of the full-scale models in the full-scale model database 205 to simplify the model. For example, a dimensionality may be reduced, one or more variables (e.g., a parameter and/or initial-state variable) may be approximated, a non-linearity may be eliminated or simplified, etc. The offline surrogate geophysical model generator 210 may modify the one or more of the full-scale models, e.g., by applying theoretical and/or sampling techniques. In some instances, an expansion and/or decomposition is applied. For example, a Karhunen Loève expansion, a decomposition (e.g., a proper orthogonal decomposition), and/or a polynomial chaos expansion may be used for developing a surrogate model.

In some instances, the modification may be, e.g., based on analysis of empirical data. The empirical data may be data from a well-site of interest, a geographic region of interest, a depth of interest, a time of interest, etc. For example, data from a near-by well drilled within the last month may be analyzed by the model generator 210. Offline surrogate geophysical model generator 210 may generate a model using. e.g., a particle-filtering technique, Bayesian technique, an iterative predictive-assessing technique, a probability sampling technique, a components-based technique, an information-theory based technique, etc. Particular non-limiting examples of surrogate model generation techniques are provided below. The modified model may include fewer unknowns and/or variables, be of a smaller order, include fewer nonlinear components, etc. as compared to a corresponding full-scale model. Thus, it may be less computationally taxing and/or more feasible to solve a surrogate model than a corresponding full-scale model. For purposes of this application the term a “surrogate” model may comprise a simplified or easier-to-solve model. For example, a surrogate model may include a same number of unknown variables, though the inferences from the model may include stricter constraints on and/or use additional information related to possible values of the variables. In an embodiment of the present invention, all available a priori information regarding the unknown variables is used for estimation purposes.

The models generated by the offline model generator 210 are transmitted to the real-time geophysical characteristic estimator 215, which may use the model to estimate a geophysical characteristic. The geophysical characteristic may be related to drilling for resources (e.g., oil and/or natural gas), extraction of resources, cuttings transport, etc. The geophysical characteristic may include one or more variables such as, e.g., a composition of a fluid or gas, a contribution (e.g., of oil or natural gas) to a fluid or gas composition, a flow rate, a cuttings' concentration, a formation resistivity, a formation's natural gamma ray, drilling-hole inclination and/or direction, a drill bit's direction, vibration, a drilling acceleration, an underground temperature, a fluid's friction coefficient, etc.

The geophysical characteristic estimator 215 may include a real-time input receiver 220, which receives real-time or near-real-time data. The input receiver 220 may, e.g., be or comprise a receiver (e.g., transmitter/receiver 36A) that receives data from one or more underground sensors, e.g., via a wired drill pipe, a receiver (e.g., transmitter/receiver 36B) that receives data from a transmitter coupled to one or more underground. In some instances, a recording unit (e.g., recording unit 38) comprising a processor, etc. The received data may comprise, e.g., electrical, optical and/or radio signals. The received data may comprise, e.g., continuous signals, discrete signals, one or more binary values, one or more numeric values, etc. For example, the received data may comprise a continuous and/or discrete pressure readings, temperature measurements, accelerations, etc. The input receiver 220 may receive signals from, e.g., a wireless transmitter, a physical transmission (e.g., via a wire or cable), etc. In some instances, the input receiver 220 receives signals from a storage medium.

The real-time input receiver 220 may transmit the received data to a model-based estimator 225, which may apply one or more surrogate geophysical models. The applied model(s) may be and/or may have properties (e.g., order reductions, term approximations, initial state estimates, etc.) determined by the offline surrogate geophysical model generator 210. Thus, the model-based estimator may be able to apply one or more models relatively quickly as compared to a comparable application of one or more corresponding full-scale models. Application of the model may result in, e.g., an estimation of one or more variables, properties or states. The model may be applied, e.g., by using part or all of the (raw or processed, e.g., filtered) received data as independent variables and applying one or more equations to calculate an estimate of one or more dependent variables. In some instances, the model may be applied by using part or all of the (raw or processed) received data as dependent variables and using inverse solution techniques to estimate values of variables that may have produced the dependent variables. The model may be applied by iteratively sampling a space and comparing possible outcomes to the received data.

Outputs of the model are transmitted to a real-time estimate output 230. The outputs may include an estimate (e.g., a value, a range of possible values, a selected value from a list of possible values, a distribution of possible values) of one or more variables (e.g., geophysical variables). Values may or may not be numeric (e.g., instead, e.g., a value may identify one of a plurality of states). The outputs may include an uncertainty and/or confidence measure. In some instances, an uncertainty and/or confidence measure may be inherently present in a distribution of possible values. In some instances, it is a separate measure. For example, an output may include a range of values and an indicator that the range corresponds to a 95% confidence interval. The output may be an estimate of a value (e.g., a numeric value) of a current or past geophysical characteristic and/or a prediction of a future geophysical characteristic or data. The output may be an estimate of an unmeasurable characteristic or a characteristic that is difficult or costly to measure. In one instance, the output comprises a prediction of data that will later be received and/or analyzed (e.g., one or more sensor readings). The output may include an estimate of, e.g., a composition of a fluid or gas, a contribution (e.g., of oil or natural gas) to a fluid or gas composition, a flow rate, a cuttings' concentration, a formation resistivity, a formation's natural gamma ray, a drilling-hole inclination and/or direction, a drill bit's direction, a vibration, a drilling acceleration, an underground temperature, a fluid's friction coefficient, etc.

Real-time estimate output 230 may present the output to a user. For example, the output may be displayed (e.g., on a screen). The output may be printed. In some instances, real-time estimate output 230 transmits the outputs (e.g., to a user device, to a wireless transceiver, etc.). In some instances, real-time estimate output 230 transmits the outputs to a controller that assesses the outputs, and identifies an appropriate strategy (e.g., resource drilling or extraction strategy) or strategy modification based on the assessed outputs. The strategy may include, e.g., pausing drilling operations, modifying a pump rate of mud, modifying a drill speed, etc. The strategies or modification may be automatically (e.g., and immediately) implemented, or the identified strategies or modifications may be presented to an operator as a suggestion or instruction.

FIG. 3 illustrates a flowchart of an embodiment of a process 300 for estimating a geophysical characteristic. At block 305, one or more full-scale geophysical models are accessed. For example, one or more models may be generated based on empirical data or retrieved from a storage medium. The full-scale model(s) may include a model retrieved from, e.g., full-scale model database 205.

At block 310, one or more surrogate geophysical model may be generated, each surrogate model corresponding to a full-scale model. The surrogate model may be generated offline, such that, e.g., data analyzed in determining the surrogate model is not real-time data (e.g., and is instead stored data). The surrogate model(s) may be generated using. e.g., a particle-filtering technique, a Kalman-filtering technique, an Ensemble-Kalman-filtering technique, a Bayesian technique, an iterative predictive-assessing technique, a probability sampling technique, a components-based technique, an information-theory based technique, etc. The modified model may include fewer unknown variables, be of a smaller order, include fewer nonlinearities, etc. as compared to a corresponding full-scale model. Thus, it may be less computationally taxing and/or more feasible to solve a surrogate model (or obtain estimates of solutions) than a corresponding full-scale model.

At block 315, real-time or near real-time geophysical inputs are received. The geophysical inputs may comprise, e.g., data from underground sensors, data from sensors coupled to resource-drilling or resource-extraction efforts, data from wire-drill-pipe sensors, etc. The inputs may be received, e.g., via transmission over a physical element (e.g., via a wire or cable) or via a wireless transmission.

At block 320, the surrogate model(s) are applied to the inputs. For example, the inputs can be used to solve for or estimate one or more unknowns or variables in the model(s). In some instances, a single model is applied to the inputs. In some instances, multiple models are applied to the inputs. The multiple models may be, e.g., complementary or alternative models. Applying the model may involve, e.g., solving one or more equations, implementing a multiple-iteration technique (e.g., assuming different potential values of variables or assuming different noise contributions), etc.

At block 325, an estimate of a geophysical characteristic is output. The estimate may include, e.g., a value, range, distribution, etc., e.g., for a variable in the surrogate model. The estimate may correspond to an estimate of a current value of a variable or a prediction of a future value of a variable. The estimate may include a confidence or uncertainty metric. The estimate may be quantitative and/or qualitative. The estimate may be, e.g., presented to a person (e.g., an operator) or transmitted to a device or device component. In some instances, output of the estimate results in an immediate implementation of a strategy (e.g., a drilling strategy) or a strategy modification.

FIG. 4 depicts a block diagram of an embodiment of a geophysical-model generator system 400. In some embodiments, in addition to or instead of estimating geophysical characteristics, a model may be modified in real-time. One or more initial models may be identified. For example, offline surrogate geophysical model generator 210 may access full-scale model database 205 and generate a corresponding surrogate model, as described above.

Based on the surrogate model, geophysical data predictor 435 may predict the probability of observing particular values of variables in the future. For example, the geophysical 20 data predictor 435 may predict that there is a 35% probability of receiving a real-time pressure reading within a particular range, or a 5% probability of receiving a pressure reading within a first range and a simultaneous temperature reading within a second range. In some instances, geophysical data predictor 435 predicts the probability that the model, as applied to real-time inputs, will produce one or more particular outputs. For example, there may be a 90% probability that the model will subsequently predict that an estimated drill-tip orientation within 10 degrees of a previous estimated drill-tip orientation. The prediction may comprise a range, a distribution, one or more numeric values, etc.

The prediction is provided to a Bayesian inference analyzer 440. The Bayesian inference analyzer 440 also receives one or more real-time or near-real-time variables, which may include a raw or processed inputs received by real-time input receiver 220. For example, the Bayesian inference analyzer 440 may receive real-time or near-real time sensor readings. In some instances, Bayesian inference analyzer 440 receives one or more outputs of a model (e.g., the surrogate model generated by offline surrogate geophysical model generator 210), after the real-time or near-real-time inputs were processed by the model. The Bayesian inference analyzer 440 may analyze the real-time or near-real-time variable in view of one or more predictions from the geophysical data predictor 435. Thus, for example, the Bayesian inference analyzer 440 may identify what the model's prediction was for the particular real-time or near-real-time variable(s).

In some instances, the geophysical data predictor 435 may apply an evolving model, such that “future” values of variables, e.g., X_(i+1), (e.g., values not yet available to the geophysical data predictor and/or not yet measured by sensors) are predicted based current, X_(i), and/or past, X₁ . . . X_(i−1), values of variables (e.g., values available to the geophysical data). Once the future values are measured and/or available (e.g., to Bayesian Inference Analyzer 440), the actual values may be compared to the predicted values.

While FIG. 4 shows a Bayesian inference analyzer 440 may apply a Bayesian-inference technique to analyze the predictions and/or may use one or more other techniques. For example, the analyzer may assess a probability distribution (e.g., within one or more predictions), apply a Bayesian-inference technique, apply a Monte-Carlo technique, apply a particle-filter technique, etc. In some instances, the analysis may assess whether an input received by the real-time input receiver 220 would have been reasonably expected based on a probability distribution determined by the geophysical data predictor 435 (e.g., by applying a noise-based simulation or distribution-sensitive equation).

In some instances, an analyzer may compare predictions from the geophysical data predictor 435 to received inputs via, e.g., standard-error calculations, information-theory approaches (e.g., assessing how informative the predictions were as to what the measurements would be), a best-fit or correlation technique (e.g., determining a quality-of-fit metric when comparing a plurality of inputs to a plurality of matched predictions, each data point being associated with a different sensor, time stamp, etc.), a cost-based metric (e.g., quantifying a “cost” of transforming the predictions to conform with received inputs), etc. The analysis may include determining one or more quantitative and/or qualitative results. The results may indicate or estimate an accuracy of the prediction.

The analysis may directly compare one or more predictions to one or more inputs (e.g., sensor measurements). In some instances, the comparison is indirect. For example, the inputs may be processed (e.g., filtered, transformed, combined, etc.) before comparing them to the predictions and/or the predictions may be processed before comparing them to the (processed or unprocessed) inputs.

The Bayesian inference analyzer 440 and/or a model adjustor 445 may identify particular model features (e.g., order reductions, variable approximations, inclusion or exclusion of nonlinearities) which would have improved the prediction or substantially maintained the prediction while simplifying the model. For example, if multiple predictions were accurate, and the predictions assumed different values for one variable, it may be assumed that the variable's value were relatively non-important in making the prediction. As another example, if accurate predictions were associated with a particular value for a variable and inaccurate predictions were associated with other values, it may be assumed that the variable should be set to the particular value. The identification may be at least partly based on any training data used by the offline surrogate geophysical model generator 210 while generating an initial model. The identification may further prioritize various simplifications (e.g., reduced orders, approximations, etc.) to limit the degree to which it may be difficult or impossible to apply a modified model in real-time.

Based on the analysis performed by the Bayesian inference analyzer 440, the model adjustor 445 may adjust the surrogate model to create a modified model. For example, a dimensionality controller 450 may control a number of non-fixed variables in the model and/or which variables in the model are fixed (e.g., the dimensionality controller 450 may determine that a particular coefficient should be fixed to a single approximation or should be constrained to values within a particular range or list). A variable approximator 455 may approximate a value for one or more variables in the model. The approximation may include, e.g., a particular value, a list of possible values, an open-ended or closed-ended range of possible values, etc. Further, the model adjustor may control a state of the model.

Using the modified model, a new prediction may be made by geophysical data predictor 435, and the Bayesian inference analyzer 440 may then compare the new prediction with one or more subsequently received real-time or near-real-time variables. In this manner, a model may be continually adjusted in real-time.

FIG. 5 illustrates a flowchart of an embodiment of a process 500 for generating geophysical models. At block 505, one or more full-scale geophysical models are accessed. At block 510, one or more surrogate geophysical models are generated based on the full-scale geophysical model(s), as described herein. As block 515, one or more predictions for each of one or more real-time variables is made based on the surrogate models. For example, a prediction may include that data received from a sensor would be within a particular range. As another example, the prediction may include a distribution identifying a predicted probability of receiving a real-time variable of various values. The prediction may be for a single variable (e.g., a sensor measurement or a processed sensor measurement) or for multiple variables (e.g., simultaneously or substantially simultaneously received or recorded measurements from multiple sensors).

At block 520, one or more prediction-matched real-time or near-real-time variables are accessed. A “prediction-matched variable” is a variable in a format that allows the variable to be compared to the prediction. For example, the prediction-matched variable and the prediction may include similar or same units (e.g., degrees—Fahrenheit or Celsius), be related to similar or same properties (e.g., temperature), etc. The accessed variables may be, e.g., raw sensor data or processed sensor data. For example, the sensor data may be filtered, decomposed, transformed, etc. In some instances, the sensor data input into a model (e.g., one or more surrogate models) to estimate the prediction-matched variables.

At block 525, a Bayesian-inference analysis is performed. The Bayesian-inference analysis compares the prediction-matched real-time variable(s) accessed at block 520 to the prediction(s) generated at block 515. Thus, the analysis may estimate whether the prediction was accurate. For example, if a prediction predicts that temperature readings will remain within a 2° F. range for a period of time, and the temperature then jumps 10° F. the prediction may be determined to have been a poor prediction. Bayesian-inference techniques—which can further include detailed calculations of a precise probability of observing the real-time variable based on the prediction—can quantify the quality of the prediction in a more quantitative manner. In some instances, the surrogate geophysical model may thereafter be adjusted in an attempt to improve prediction quality and more accurately model geophysical characteristics.

Thus, at block 530, the surrogate geophysical model is adjusted. In some instances, the adjustment is always made when the Bayesian-inference analysis determines that the adjustment would improve future predictions. In some instances, possible adjustments are constrained. For example, there may be constraints on a frequency of adjustments or magnitude of adjustments. There may be constraints to prevent or reduce the probability of adjustments that would lead to, e.g., a high-dimensionality model, a model with many nonlinear terms, a model which could not be applied in real-time, etc.

Part of all of process 500 may be repeated. For example, FIG. 5 shows a repetition of blocks 515-530, wherein the next prediction is made using the adjusted surrogate model.

FIG. 6 depicts a block diagram of an embodiment of a model-modification system 600. For example, the system 600 may be used to modify a full-scale model to produce a surrogate model, to adjust a surrogate model in real time, etc. Model identifier 610 identifies a model. The identified model may include, e.g., a model from the full-scale model database 205. In some instances, the identified model is a surrogate model (e.g., received from the offline surrogate geophysical model generator 210.

A space definer 615 defines a space associated with each unknown variable associated with the identified model. For example, a space may be defined for each unknown parameter and/or each unknown state (e.g., a current-value or initial-value state). A space may include one or more ranges of possible values, one or more types of values, a distribution within a range of possible values, etc. For example, a space for one parameter may include all real numbers and the probability distribution may be a Gaussian distribution with a particular mean and standard deviation. As another example, a space for one parameter may include all integers from 1-10. A space may be multidimensional. For example, a first parameter may have a one probability distribution when a second parameter is below a threshold and a another probability distribution otherwise.

A particle sampler 620 may sample the space and characterize a particle. Each particle may be associated with a value for each unknown variable (e.g., unknown parameter and/or state). The values may be randomly selected from the defined space. Thus, for example, if a space associated with one variable comprises a Gaussian distribution, the value for that variable for one particle may be randomly selected from amongst the Gaussian distribution. This process may be repeated many times, such that a set of particles is generated.

The particles and identified model are transmitted to the model-based estimator 225. For each particle, the identified model may be applied. Additional input values may be provided to the model from a training-data database 625. The training-data database 625 may include empirical data. The data may include data collected from a particular location of interest, a particular drill site, a particular type of resource extraction (e.g., oil well), etc. The data may include recently collected data, data collected using equipment of interest, data collected by sensors of interest or by sensors of a type of interest, etc. Thus, based on the provided input and the values associated with each particle, the model-based estimator 225 may output a prediction for each particle. The prediction may include, e.g., a single value, a range of values, a distribution, etc.

The prediction may be analyzed by a model output analyzer 630. The model output analyzer 630 may compare the prediction to an output (e.g., training-data output, received from the training-data database 625; subsequently received real-time data; etc.). The compared output may include, e.g., a time-evolved output, such that the output is associated with a time beyond a time associated with the input. The output and input may or may not be a same type of variable. The output and/or the input may or may not comprise one or more sensor readings. The model output analyzer 630 may e.g., use a Bayesian-inference technique to compare the model's prediction with the training-data output. The model output analyzer 630 may assess whether the prediction of the model was a good prediction of the training-data output.

Based on the analysis performed by model output analyzer 630, a particle weight assigner 635 may assign a weight to each particle. For example, particles which led to accurate model-based predictions of the training-data output may be heavily weighted. The weighting may be, e.g., continuous and/or discretized. For example, the weights may vary continuously from 0 to 1, or the weights may be either 0 or 1 with no possible in between values. Assignments of the weights may involve comparison to a threshold. For example, if a difference between a model-based prediction and the training-data output exceeded a threshold, the particle may be assigned a weight of “0”. The weight may otherwise be, e.g., “1” or determined based on a continuous scale.

The assigned weights may be transmitted to the space definer 615. The space definer 615 may then adjust the spaces based on the weights. For example, if each particle from one group of particles were assigned low weights and had common values of a parameter, then the space may be adjusted to reduce a probability associated with that portion of the parameter's space. Adjustments may depend, e.g., on weight values and particle samplings.

Based on the adjusted space, the identified model may be modified by model modifier 640. For example, eventually a space associated with a particular parameter may become small (e.g., smaller than a threshold condition) or non-existent (e.g., converging to a single value). Based on reductions or concentrations of clouds, the model modifier may then simplify the model. In some instances, nonlinearity terms may be eliminated or simplified by a nonlinearity simplifier 645. In some instances, a dimensionality or order of the model may be reduced by a dimensionality reducer 650. The model modification may further involve approximating one or more terms (e.g., determining a value for each of one or more variables) in the model.

FIG. 7 illustrates a flowchart of an embodiment of a process 700 for modifying models. The model modification can be performed, e.g., offline using training data. At block 705, a model is identified. The model may include, e.g., a full-scale model or surrogate model. At block 710, one or more clouds are identified. Each cloud, e.g., may characterize potential values of parameters and/or state conditions. The cloud may include, e.g., a probability distribution, outer range, etc.

At block 715, one or more particles are sampled from the cloud. In preferred embodiments, a plurality of particles are (e.g., simultaneously or substantially simultaneously) sampled from the cloud—though, in some embodiments, the particles are iteratively sampled such that the model is applied to each particle prior to sampling of another. At block 720, the model is defined based on values associated with the particle and applied to input data. For example, the input data may comprise training-data input, which may include, e.g., real or simulated sensor readings. The model may output. e.g., a prediction.

At block 725, the model's prediction may be compared to training output. For example, a probability of observing the training output may be determined based on the prediction, or a difference between a prediction and the output may be determined. At block 730, a weight is assigned to each sampled particle based on the comparison. For example, particles for which the prediction was highly accurate may be relatively highly weighted. Based on the assigned weight, a new cloud of parameters and/or state conditions may be identified and blocks 710-730 may be repeated. At block 735, a model's dimensionality is reduced. For example, possible parameter values may be bounded, one or more parameters may be approximated and fixed within the model, parameters co-variation may be constrained, etc. In some instances, the reduced-dimensionality model can be subjected to further model scrutiny to further validate the modified model. The modified model can be used in real-time or non-real-time to estimate a geophysical characteristic.

FIG. 8 a depicts a block diagram of an embodiment of a system 800 a for estimating a geophysical characteristic. The model(s) may include, e.g., one or more surrogate geophysical models generated by offline surrogate geophysical model generator 210 based on an analysis of one or more full-scale models 205. In some instances, a plurality of models are identified. The models may have, e.g., a different dimensionality, a different order, different inputs, different outputs, etc. For example, one model may be configured to receive inputs from Sensors 1-5; another model may be configured to receive inputs from Sensors 1-4: another model may be configured to receive inputs from Sensors 1-3 and 5; another model may be configured to receive inputs from Sensors 1-2; etc. Each model may, e.g., correspond to a different operational state. For example, one model may correspond to a default or proper operation of a drilling operation; another model may correspond to operation in which one sensor is unavailable; another model may correspond to operation in which all sensors are unavailable; another model may correspond to a lost-circulation operation; another model may correspond to one or more sensors having a bias in their measurements (e.g., a D.C. offset): etc. In some instances, a single model may include a parameter that reflects an operational state and/or sensor availability; etc.

The identified model is transmitted to the geophysical data predictor 435. The geophysical data predictor 435 may, in some instances, also receive geophysical input. The geophysical input may include, e.g., real-time or near-real-time input received by a real-time input receiver 220. The geophysical input may include cached or stored data. The geophysical input may include training data. The geophysical input may include readings from one or more sensors and/or a state of one or more sensors (e.g., properly operating, failed transmission, etc.) The geophysical data predictor 435 may determine one or more predictions. The one or more predictions may include, e.g., one or more sensor readings (e.g., associated with a time after a time associated with an analyzed input).

Model analyzer 860 may analyze one or more models and/or one or more predictions made based on the model(s) in view of empirical geophysical data. The empirical geophysical data may be, e.g., stored in an empirical geophysical data database 840 or directly received, e.g., from a transmitter without first being stored. The empirical geophysical data may be matched to the prediction made by the geophysical data predictor 435, e.g., such that the prediction and data may be compared to assess a quality of the prediction. The model analyzer 860 may assess the quality of one or more predictions as described herein (e.g., by analyzing the empirical geophysical data in view of a predicted probability distribution, etc.).

The empirical geophysical data may include, e.g., one or more sensor readings and/or availability or states of one or more sensors. The model analyzer 860 may compare inputs (e.g., qualitative features of the inputs) of one or more models to the empirical geophysical data. For example, the model analyzer 860 may determine that Model #1 has five inputs, corresponding to readings from Sensors 1-5; and that Model #2 has four inputs, corresponding to readings from Sensors 2-5. The model analyzer 860 may further determine, based on the empirical geophysical data 840 that readings from Sensor #1 are unavailable, unreliable, exceeding a threshold, etc. In some instances, the model (or a model parameter) and the empirical geophysical data comprise a state variable. The model analyzer 860 may analyze these state variables. For example, Model #1 may be indexed as a “Vertical Drilling” model; Model #2 may be indexed as a “Horizontal Drilling” model; Model #3 may be indexed as an “Inclined Drilling” model; Model #4 may be indexed as a “Lost Circulation” model: Model #5 may be indexed as a “Sensor Failure” model; Model #6 may be indexed as a “Catastrophic Failure” model, etc. The empirical geophysical data may include a state variable (e.g., which can be entered by an operator) and/or may include one or more variables indicative of a state.

Based on the analysis performed by the model analyzer 860, a weight assigner 865 may assign weights to one or more models, one or more parameters, one or more value probabilities, one or more model-based particles, one or more space estimates, etc. In some instances, assigning a weight comprises selecting a model, a parameter value, etc. For example, the weight assigner selects a surrogate model from a plurality of surrogate models; one of a plurality of state values for a state parameter, an availability value (e.g., a binary value) for an availability parameter associated with each of one or more sensors, a value (e.g., an integer) for a number-of-available-sensors parameter, etc. In some instances, the geophysical data predictor may output a plurality of particles. Different particles may be, e.g., associated with different models, parameter values, states, etc. Based on an analysis performed by the model analyzer 860, the weight assigner 865 may assign a weight to each particle.

Weight assignments (e.g., model selection, parameter-value selection, particle weighting, etc.) may be based on, e.g., a match (e.g., above-threshold similarity, highly ranked similarity, best matched) to a number of inputs (e.g., one model includes five inputs and five deemed-reliable geophysical sensor readings are available); a state associated with a model, particle, parameter, etc.; an above-threshold, best or adequate prediction made by the geophysical data predictor 435 using a model; previous selections or weights; predicted computational speed or efficiency; etc.

In some instances, the system 800 regularly evaluates a plurality of models or parameters. For example, the system 800 may routinely assess a number of available inputs compared to a number of inputs associated with each available model. In some instances, the system 800 initially evaluates a subset (e.g., one) of the models or parameters and may subsequently evaluate other models or parameters. For example, the system 800 may regularly assess whether a currently selected model adequately represents an estimated state corresponding to input. If, e.g., the model detects that the selected model is not predicting data with sufficient accuracy, or if the inputs received are not matched to inputs required for the selected model, a new model may be assessed.

System 800 may further include a model-based estimator 225 to estimate one or more values for one or more geophysical characteristics. The estimated values may be based at least partly on the weights assigned by weight assigner 865. For example, the estimated values may include values estimated assuming one or a subset of operational states and/or sensor states, the one or subset being determined based on the assigned weight. The estimated values may include a single value for each geophysical characteristic (e.g., a flow rate at a particular depth equal to a flow rate estimated assuming a specific operational state and/or sensor state) or a probability distribution (e.g., the distribution based on the weights assigned to estimations made assuming a variety of operational states and/or sensor states). The estimated values may comprise hidden or observable values. In some instances, the estimated values comprise the same types of values as those predicted by geophysical data predictor. (Thus, in some instances, the model-based estimator 225 replaces the geophysical data predictor 435 after one or more initial iterations.)

In some instances, the estimated values comprise different types of values as those predicted by geophysical data predictor. For example, the model-based estimator 225 may determine highly weighted parameter values corresponding to an operational-state and/or sensor-state variables and apply one or more models, or the model-based estimator 225 may determine a highly weighted model and apply the model. In some instances, estimates are generated assuming each of a plurality of operational states and/or sensor states, and the model-based estimator 225 selects, compiles or processes the estimates based on the weights.

The estimated one or more values for the one or more geophysical characteristics are the output in real-time or near real-time by real-time estimate output 230. For example, the output may be displayed (e.g., on a screen). The output may be printed. In some instances, real-time estimate output 230 transmits the outputs (e.g., to a user device, to a wireless transceiver, etc.). In some instances, real-time estimate output 230 transmits the outputs to a controller that assesses the outputs, and identifies an appropriate strategy (e.g., resource drilling or extraction strategy) or strategy modification based on the assessed outputs. The strategy may include, e.g., pausing drilling operations, modifying a pump rate of mud, modifying a drill speed, etc. The strategies or modification may be automatically (e.g., and immediately) implemented, or the identified strategies or modifications may be presented to an operator as a suggestion or instruction.

FIG. 8 b depicts a block diagram of an embodiment of a system 800 b for estimating a geophysical characteristic. Many blocks parallel those in FIG. 8 a, and pertinent related disclosures are contemplated for this embodiment as well. System 800 b includes a multi-state model-based estimator 870. Based on one or more geophysical models, multi-state model-based estimator generates a plurality of estimates pertaining to a geophysical characteristic. The estimates may be for a current time-stamp variable value or a future time-stamp variable value.

The estimates may assume an operational state and/or a sensor state. For example, one estimate may assume a normal-operation state, another may assume a paused-drilling state, another may assume a potential lost-circulation state, another may assume a catastrophic-event state, etc. In some instances, different models are associated with different operational states and/or sensor states. For example, generating an estimate using Model #1 may result in generating an estimate assuming a normal-operation state. In some instances, a parameter relates to an operational state and/or sensor state. For example, generating an estimate using a value of “1” for a parameter may cause the estimate to assume normal operation, and generating an estimate using a value of “2” for the parameter may cause the estimate to assume suspect sensor readings.

In this embodiment, at least two of the estimates assume different states. For example, one or more first estimates may assume a normal operation state, one or more second estimates may assume a state in which sensor #4 is malfunctioning, and one or more third estimates may assume a state in which at least one sensor is biased. In this embodiment, real-time estimates are generated for each of the plurality of estimates. Though each estimate may involve computationally expensive techniques (e.g., repeated Monte-Carlo-based iterations), multiple real-time estimates may be feasible due to use of one or more surrogate (or otherwise simplified) geophysical models.

An operational state identifier 875 may estimate a current or future operational state and/or sensor state (e.g., a state for a current, next or future time stamp). The estimate may include a single state, weighted probabilities of multiple states, a subset of states, etc. For example, the state identifier may estimate that a current state is a State #1; or that there is a 90% probability that it is State #1, 8% probability that it is State #2, 2% probability that it is State #3, and 0% probability that it is State #4; or that it may be any of States #1-5, but none of States #6-10.

Operational state identifier 875 may estimate the state(s) in a variety of manners. The estimated state may depend on real-time or near real-time inputs received by real-time input receiver 225. In one instance, an operator inputs a state. In one instance, an analysis of sensor measurements (e.g., to identify measurement availability, DC bias, suspected malfunction based on constant readings, etc.) is performed by the operational state identifier 875 and/or another component and influences the estimated state. The estimated state may depend on previously estimated states (e.g., to bias towards similar state estimates) and/or on one or more default states (e.g., a normal-operation state).

Based on the identified operational and/or sensor state(s), one or more weights may be assigned by the weight assigner 865. As described above, the weights may be normalized, along a continuum, binary, etc. In some instances, one, two, three or more weights are set to a non-zero value, and the rest of the weights are set to a zero value.

A fine-tuned model-based estimator 880 may the generate an estimate of a geophysical characteristic based on the initial estimates generated by the multi-state model-based estimator 870 and the weights assigned by the weight assigner 865. For example, the fine-tuned model-based estimator may select one or a subset of the estimates generated by the multi-state model-based estimator 870. In some instances, the selected estimate(s) (e.g., along with associated confidence or certainty metrics and/or weights) are output from the fine-tuned model-based estimator to be output by the real-time estimate output. The estimates may or may not be processed (e.g., to create a weighted average of the estimates, a certainty or confidence metric based on the estimates, a probability distribution, etc.) by the fine-tuned model-based estimator 880.

The fine-tuned estimate(s) may then be output by the real-time estimate output 230, e.g., as described, herein. This embodiment allows estimates to be repeatedly generated assuming each of a variety of states. Models (assuming each of the states) may then gradually build upon data received over an extended time period. Thus, upon a determination that a state changed from “Normal-Operation” to “Lost Circulation”, a lost circulation model may have been gradually and continually adapting its features (e.g., values of its model parameters, nonlinearity features, etc.), such that it can generate estimates based on the most recent data. Meanwhile, the output of the system remains specific to an estimated operational and/or sensor state.

In FIGS. 9 a-9 c illustrate flowcharts of embodiments of processes for estimating one or more geophysical characteristics. In these processes, a plurality of variables are calculated in real-time, each assuming one or more operational states and/or sensor states. An estimated operational and/or sensor state is then explicitly, implicitly or inherently determined, e.g., accuracies of at least some of the variables that serve as predictions of other variables (e.g., as predictions of future sensor measurements), by input from an operator, an automatic process (e.g., identifying a sensor's reliability, etc.). A real-time estimate of a geophysical characteristic is then determined based on the estimated operational and/or sensor state. Thus, the process has the capability to repeatedly determine estimations or predictions assuming different operational and/or sensor states and then tailor its output of geophysical characteristics based on explicitly, implicitly or inherently determined an operational and/or sensor state. Use of surrogate models may enable the repeated estimations or predictions assuming the different states to be performed in real-time or near real-time.

FIG. 9 a illustrates a flowchart of an embodiment of a process 900 a for estimating one or more geophysical characteristics. At block 905, one or more full-scale geophysical models are accessed. At block 910, one or more surrogate geophysical models are generated (e.g., offline) based on the full-scale geophysical models. At block 915, real-time geophysical inputs are accessed. The inputs may include, e.g., measurements from one or more sensors.

At block 922, a plurality of predictions or estimate are generated, each prediction predicting or estimate estimating one or more (e.g., future or current) real-time variables. For example, an estimate may estimate a hidden variable for a time stamp associated with the accessed real-time geophysical inputs, or a prediction may predict a hidden or observable variable (or variable derivable from observable data) from a time stamp after the time stamp associated with the accessed real-time geophysical inputs.

Each prediction or estimate is based on one or more models, and some or all of the predictions or estimates may, or may not, be based on the same model(s). Each prediction or estimate assumes an operational state and/or sensor state. For example, one or more variables in one or more models may indicate an operational and/or sensor state (e.g., a model's variable could include a binary variable for each sensor indicating whether sensical measurements are being received). As another example, each of a plurality of models assumes a different operational state and/or sensor state, and the predictions assume the state based on application of particular model(s). The predictions or estimations may be for a value of a hidden or observable value. In one instance, the predictions indicate values for to-be-collected or to-be-accessed sensor measurements.

At block 945, a weight is assigned to the predictions or estimations. The weight may or may not be based on the predictions or estimations themselves. For example, in one instance, an accuracy of the predictions is later assessed, and accurate predictions are highly weighted. In another example, an operator identifies an operational state, and predictions associated with the operational state are highly weighted.

At block 950, one or more real-time estimate(s) of one or more geophysical characteristics are determined based on the assigned weight. The estimate(s) may include, e.g., a value, range, distribution, etc., e.g., for a variable in the surrogate model. The estimate(s) may correspond to an estimate of a current value of a variable or a prediction of a future value of a variable. The estimate(s) may include a confidence or uncertainty metric. The estimate(s) may be quantitative and/or qualitative.

In some instances, the one or more geophysical characteristics comprise the generated predictions or estimations. For example, the one or more geophysical characteristics could comprise a probability distribution of values of the real-time variable(s), the distribution being based on the assigned weight. In another example, the geophysical characteristics could comprise a list or a single value of the geophysical characteristic, the value being equal to a value predicted at block 922.

In some instances, the one or more geophysical characteristics do not comprise the generated predictions or estimations. For example, the generated predictions may relate to observable variables, and the geophysical characteristics may relate to hidden variables. Values of geophysical characteristics may be determined for each of a plurality of operational states and/or sensor states, and the determined real-time estimate(s) may comprise a selected value or combination of values (e.g., a probability distribution based on the values). In some instances, the geophysical characteristics are not determined until the weight has been assigned. Thus, for example, only one or a subset of the operational states and/or sensor states need be assumed to generate respective the geophysical characteristic(s).

At block 955, one or more real-time or near real-time estimates of one or more geophysical characteristics is output. The estimate(s) may be, e.g., presented to a person (e.g., an operator) or transmitted to a device or device component. In some instances, output of the estimate results is an immediate implementation of a strategy (e.g., a drilling strategy) or a strategy modification.

FIG. 9 b illustrates a flowchart of an embodiment of another process 900 b for generating one or more geophysical characteristics. Many blocks parallel those in FIG. 9 a, and pertinent related disclosures are contemplated for this embodiment as well.

In this embodiment, at block 920, one or more models (e.g., the surrogate geophysical models) are applied to the inputs to generate prediction(s) of real-time variable(s), generate predictions. The generated predictions may comprise predictions of values of one or more variables (e.g., sensor measurements) not yet accessible (e.g., to system 800) or measured.

At block 925, prediction-matched real-time or near-real-time data are accessed. For example, real-time or near-real-time measurements from one or more sensors may be received. In some instances, the prediction-matched variables comprise similar or same types of inputs as those received at block 915, but are associated with a later time. Thus, for example, prediction-matched data accessed at block 925 may be associated with a same time stamp as the geophysical inputs accessed at block 915 during a subsequent iteration. There may further be a partial or full overlap between the prediction-matched real-time data accessed at block 925 and the geophysical inputs accessed at block 915 during a subsequent iteration.

At block 930, the predictions and prediction-matched data are analyzed. For example, a prediction quality may be estimated, predictions may be ranked, or a particular prediction (e.g., a best prediction) may be identified.

At block 945, a weight is assigned, e.g., to one or more models, parameters, values of parameters and/or particles. The weight assignment may comprise, e.g., weighting one, more or all particles (e.g., with subsets of particles being associated with different states, models, etc.). Assigned weights may be along a continuum (e.g., any real number, any real number from 0 to 1, any real number from −100 to 100, etc.), along a discretized continuum (e.g., all integers from 0 to 10, etc.), binary, etc. In some instances, weights are normalized. In one example, all weights except for one are equal to a default value (e.g., “0” or “not selected”), and the one weight is assigned another value (e.g., “1” or “selected”). The weight assignment may comprise selecting, e.g., a current model, parameter value, etc. The weighting (e.g., which in some instances comprises a selection) may be based on, e.g., the analysis performed at block 930.

FIG. 9 c illustrates a flowchart of an embodiment of another process 900 c for generating one or more geophysical characteristics. Many blocks parallel those in FIG. 9 a and/or FIG. 9 b, and pertinent related disclosures are contemplated for this embodiment as well.

In some embodiments, the received real-time geophysical inputs comprise sensor-state and/or operational-state data. The sensor-state and/or operational-state data may comprise data automatically collected (e.g., from sensors). The sensor-state and/or operational-state data may comprise raw or pre-processed data (e.g., filtered sensor measurements; temporal properties of sensor data such as variation, temporal correlation, etc. of time-varying data; frequency-based properties of the data obtained based on transforming time-varying data into the frequency domain and identifying properties of the transformed data; etc.). In some instances, the data may include signals from sensors, wherein an operational state of the sensors may be inferred based on the signals (e.g., sensors transmitting a constant-value signal may be assumed to be malfunctioning).

In some embodiments, sensor-state and/or operational-state data may comprise data input by a human or collected after a request for the data (e.g., a human requesting a particular measurement from a sensor). In some instances, the data may indicate an operator-selected state (e.g., proper operation of the sensors; identification of which sensors are or are not properly operating; etc.).

In this embodiment, at block 935, the sensor-state and/or operational-state data is accessed. Accessing the sensor-state and/or operational-state data may comprise, e.g., identifying one or more of values in the real-time geophysical inputs or otherwise available values. Accessing the sensor-state and/or operational-state data may include processing inputs and/or available variable values to determine values, properties or states relevant to an estimate of a sensor state and/or operational state.

At block 940, the sensor-state and/or operational-state data is analyzed in view of model state features. Model state features may include, e.g., a number of inputs, a definition of one or more inputs, a model-specific state index, an operational-state parameter, a sensor-state parameter, etc. Thus, for example, the analysis may identify one or more models and/or parameter values that correspond with the accessed sensor-state and/or operational-state data. For example, if model #1 corresponds to normal operation and model #2 corresponds to emergency operation, the analysis may identify model #2 after an input identifying the emergency operation was accessed at block 935. As another example, if a sensor-analyzer determines that sensors #2 and #6 are not collecting data and that measurements from sensor #3 have a D.C. bias, the analysis may determine that a sensor-status variable for sensors #2 and #6 should be set to “0” or “inactive” and a sensor-specific bias variable should be set to an appropriate value for sensor #3.

Following this analysis, particular particles, parameter values and/or models may be assigned weights at block 945. For example, particles associated with variables consistent with the sensor-state and/or operational-state data may be highly rated. As another example, models corresponding to the accessed sensor-state and/or operational state data may be highly rated (e.g., or selected).

In some instances, real-time estimates of the geophysical characteristic(s) are generated assuming each of a plurality of operational states and/or sensor state. Following the weight assigning, the estimates are weighted or selected based on the weights, such that the real-time estimate(s) of geophysical characteristic(s) generated at block 950 and output at block 955 is biased towards one or a subset of the estimates.

It will be appreciated that embodiments disclosed herein which relate to estimating values for a geophysical characteristic can be extended to estimate one or more other variables pertaining to a resource drill site. For example, a model (e.g., at least partly constructed based on sensor readings and/or that receives sensor readings) can produce an estimate of a drilling characteristic. The drilling characteristic can characterize an operation of a piece of equipment at the resource drill site, such as a motor, bottomhole assembly, drill bit, drillstring and/or the like. The estimate can include a velocity of the piece of equipment (e.g., an angular and/or translational velocity), a force applied by the equipment (e.g., to maintain a velocity), a force or resistance applied to the equipment (e.g., by surrounding formations, fluid flow, weight acting on the equipment and/or the like), a metric indicating the equipment's consistency with regard to performance, and/or a metric indicating the equipment's efficiency. In some instances, the model does not explicitly and/or implicitly include variables pertaining to geophysical characteristics, while in some instances, it does (e.g., as intermediate or hidden variables). In some instances, the equipment-related variable(s) themselves are intermediate variables and the model produces geophysical-characteristic variable values as final model results.

Referring next to FIG. 10, an exemplary environment with which embodiments may be implemented is shown with a computer system 1000 that can be used by a designer 1004 to design, for example, electronic designs. The computer system 1000 can include a computer 1002, keyboard 1022, a network router 1012, a printer 1008, and a monitor 1006. The monitor 1006, processor 1002 and keyboard 1022 are part of a computer system 1026, which can be a laptop computer, desktop computer, handheld computer, mainframe computer, etc. The monitor 1006 can be a CRT, flat screen, etc.

A designer 1004 can input commands into the computer 1002 using various input devices, such as a mouse, keyboard 1022, track ball, touch screen, etc. If the computer system 1000 comprises a mainframe, a designer 1004 can access the computer 1002 using, for example, a terminal or terminal interface. Additionally, the computer system 1026 may be connected to a printer 1008 and a server 1010 using a network router 1012, which may connect to the Internet 1018 or a WAN.

The server 1010 may, for example, be used to store additional software programs and data. In one embodiment, software implementing the systems and methods described herein can be stored on a storage medium in the server 1010. Thus, the software can be run from the storage medium in the server 1010. In another embodiment, software implementing the systems and methods described herein can be stored on a storage medium in the computer 1002. Thus, the software can be run from the storage medium in the computer system 1026. Therefore, in this embodiment, the software can be used whether or not computer 1002 is connected to network router 1012. Printer 1008 may be connected directly to computer 1002, in which case, the computer system 1026 can print whether or not it is connected to network router 1012.

With reference to FIG. 11, an embodiment of a special-purpose computer system 1100 is shown. The offline surrogate geophysical model generator 210, real-time geophysical characteristic estimator 215, geophysical data predictor 435, Bayesian inference analyzer 440, model adjustor 445, etc. are some examples of a special-purpose computer system 1100. The above methods may be implemented by computer-program products that direct a computer system to perform the actions of the above-described methods and components. Each such computer-program product may comprise sets of instructions (codes) embodied on a computer-readable medium that directs the processor of a computer system to perform corresponding actions. The instructions may be configured to run in sequential order, or in parallel (such as under different processing threads), or in a combination thereof. After loading the computer-program products on a general purpose computer system 1026, it is transformed into the special-purpose computer system 1100.

Special-purpose computer system 1100 comprises a computer 1002, a monitor 1006 coupled to computer 1002, one or more additional user output devices 1130 (optional) coupled to computer 1002, one or more user input devices 1140 (e.g., keyboard, mouse, track ball, touch screen) coupled to computer 1002, an optional communications interface 1150 coupled to computer 1002, a computer-program product 1105 stored in a tangible computer-readable memory in computer 1002. Computer-program product 1105 directs system 1100 to perform the above-described methods. Computer 1002 may include one or more processors 1160 that communicate with a number of peripheral devices via a bus subsystem 1190. These peripheral devices may include user output device(s) 1130, user input device(s) 1140, communications interface 1150, and a storage subsystem, such as random access memory (RAM) 1170 and non-volatile storage drive 1180 (e.g., disk drive, optical drive, solid state drive), which are forms of tangible computer-readable memory.

Computer-program product 1105 may be stored in non-volatile storage drive 1180 or another computer-readable medium accessible to computer 1002 and loaded into memory 1170. Each processor 1160 may comprise a microprocessor, such as a microprocessor from Intel® or Advanced Micro Devices, Inc.®, or the like. To support computer-program product 1105, the computer 1002 runs an operating system that handles the communications of product 1105 with the above-noted components, as well as the communications between the above-noted components in support of the computer-program product 1105. Exemplary operating systems include Windows® or the like from Microsoft Corporation, Solaris® from Sun Microsystems, LINUX, UNIX, and the like.

User input devices 1140 include all possible types of devices and mechanisms to input information to computer system 1002. These may include a keyboard, a keypad, a mouse, a scanner, a digital drawing pad, a touch screen incorporated into the display, audio input devices such as voice recognition systems, microphones, and other types of input devices. In various embodiments, user input devices 1140 are typically embodied as a computer mouse, a trackball, a track pad, a joystick, wireless remote, a drawing tablet, a voice command system. User input devices 1140 typically allow a user to select objects, icons, text and the like that appear on the monitor 1006 via a command such as a click of a button or the like. User output devices 1130 include all possible types of devices and mechanisms to output information from computer 1002. These may include a display (e.g., monitor 1006), printers, non-visual displays such as audio output devices, etc.

Communications interface 1150 provides an interface to other communication networks and devices and may serve as an interface to receive data from and transmit data to other systems, WANs and/or the Internet 1018. Embodiments of communications interface 1150 typically include an Ethernet card, a modem (telephone, satellite, cable, ISDN), a (asynchronous) digital subscriber line (DSL) unit, a FireWire® interface, a USB® interface, a wireless network adapter, and the like. For example, communications interface 1150 may be coupled to a computer network, to a FireWire® bus, or the like. In other embodiments, communications interface 1150 may be physically integrated on the motherboard of computer 1002, and/or may be a software program, or the like.

RAM 1170 and non-volatile storage drive 1180 are examples of tangible computer-readable media configured to store data such as computer-program product embodiments of the present invention, including executable computer code, human-readable code, or the like. Other types of tangible computer-readable media include floppy disks, removable hard disks, optical storage media such as CD-ROMs, DVDs, bar codes, semiconductor memories such as flash memories, read-only-memories (ROMs), battery-backed volatile memories, networked storage devices, and the like. RAM 1170 and non-volatile storage drive 1180 may be configured to store the basic programming and data constructs that provide the functionality of various embodiments of the present invention, as described above.

Software instruction sets that provide the functionality of the present invention may be stored in RAM 1170 and non-volatile storage drive 1180. These instruction sets or code may be executed by the processor(s) 1160. RAM 1170 and non-volatile storage drive 1180 may also provide a repository to store data and data structures used in accordance with the present invention. RAM 1170 and non-volatile storage drive 1180 may include a number of memories including a main random access memory (RAM) to store of instructions and data during program execution and a read-only memory (ROM) in which fixed instructions are stored. RAM 1170 and non-volatile storage drive 1180 may include a file storage subsystem providing persistent (non-volatile) storage of program and/or data files. RAM 1170 and non-volatile storage drive 1180 may also include removable storage systems, such as removable flash memory.

Bus subsystem 1190 provides a mechanism to allow the various components and subsystems of computer 1002 communicate with each other as intended. Although bus subsystem 1190 is shown schematically as a single bus, alternative embodiments of the bus subsystem may utilize multiple busses or communication paths within the computer 1002.

EXAMPLES Example 1

In some embodiments, techniques, methods and systems described herein may be applied to estimate and/or predict properties related to cuttings transports. In one example, a model of a dynamic system describing cuttings transport includes the following relationship:

x _(k+1)=ƒ(x _(k) ,z _(k) ,q _(k)),y _(k) =g(x _(k) ,z _(k) ,q _(k)),z _(k+1) =z _(k)+noise,  (1)

where x_(k) is the state vector with n_(x) entries as the average cuttings volume along the annulus, z_(k) is the parameter vector with n_(z) entries as the uncertain parameters (e.g., cuttings slip velocities along the annulus), q_(k) is the input to the process (e.g., pump volumetric flow rate and rate of penetration of the bit), and y_(k) is a vector containing pressure measurements at sparse locations along the annulus. Functions ƒ and g may be functions describing the cuttings transport process based on conservation of mass and momentum respectively or other drilling related models (e.g., torque drag model, temperature models, drillstring dynamics model, hydraulics model etc). The underlying parameter z_(k) is either non-time varying or changing in time. In cuttings transport, and other oilfield processes, the dimensionalities of the state and parameter spaces, n_(x) and n_(z), may be large.

At a time instance t_(k) the Bayesian approach combines simulations from the model in Eqn. (1) and noisy sensor observations

y _(k) ^(obs) =y _(k)+noise,  (2)

to determine the probability distributions of the uncertain state and model parameters conditioned on the set of measurements up to time t_(k). Particle filtering is performed in the following steps. First a cloud (a large number) of parameters and initial state conditions (known as particles) are sampled from their prior distributions. These particles are denoted by the set {μ_(k+1) ^((i))}_(i=1) ^(N)={x_(k) ^((i)),z_(k) ^((i))}_(i=1) ^(N), where N is the number of the particles. Then, the particles are evolved in time using the forward model equations in (1), such that at a future time t_(k+1) a new cloud of N particles {μ_(k+1) ^((i))}_(i=1) ^(N)={x_(k+1) ^((i)),z_(k+1) ^((i))}_(i=1) ^(N) is obtained. Once measurement data are available, a weight is associated to the evolved particles. A large weight is given to the particles that provide a good match between the data and the model outputs, and a small weight is given to the particles that do not provide a good match. A new set of particles is then sampled from the evolved cloud of particles according to the conditional distribution

π(x _(k+1) ,z _(k+1)|data),  (3)

and the filtering operation is repeated in real-time. At each instance in time, statistical moments (e.g., mean and variance) can be obtained from the cloud of particles to quantify uncertainty.

A surrogate model, corresponding to a full-scale model associated with Eqn. (1), may be generally of the form:

{circumflex over (x)} _(k+1)={circumflex over (ƒ)}({circumflex over (x)} _(k) ,{circumflex over (z)} _(k) ,{circumflex over (q)} _(k)),y _(k) ≈ĝ({circumflex over (x)} _(k) ,{circumflex over (z)} _(k) ,{circumflex over (q)} _(k)),{circumflex over (z)} _(k+1) ={circumflex over (z)} _(k)+noise,  (4)

where {circumflex over (x)}_(k),{circumflex over (z)}_(k) are low dimensional state and parameter vectors, and functions {circumflex over (ƒ)} and ĝ are inexpensive surrogate functions of ƒ and g describing the original model.

A combination of Karhunen Love expansion were used for the reduction in the parameter space, a proper orthogonal decomposition was used for the reduction in the state space and generalized polynomial chaos expansions were used for the approximation of nonlinearities.

Example 2

Cuttings transport process in a vertical wellbore annulus in oilfield drilling are considered. Considering conservation of mass and a simplified version of linear momentum the process is described by a set of partial differential equations in one dimensional domain D_(s)≡as, {0≦L≦L} as,

$\begin{matrix} {{{\frac{\partial\left( {\rho_{r}x_{r}} \right)}{\partial t} + \frac{\partial\left( {\rho_{r}x_{r}v_{r}} \right)}{\partial s}} = {\rho_{r}q}},\mspace{14mu} {{\frac{\partial(p)}{\partial s} + {\rho \; g} + f_{sh}} = 0},} & (5) \end{matrix}$

where s is the distance along the annulus from the surface, x_(r)(s, t) is the volumetric concentration of the cuttings, ρ_(r)(s), ρ(s) are the densities of the cuttings and the density of their mixture with mud, respectively. The variable, ν_(r)(s, t), is defined as the velocities of the cuttings, q(s, t) as the rate of cuttings volume production (a function of the rate of bit penetration and bit diameter), p(s, t) as the pressure along the annulus and ƒ_(sh) is a pressure loss term due to shear stress. Discretizing the domain D_(s) in n cells around n nodes at depths s_(i)εD_(s), for i=1, . . . n, and applying an upwind finite volume discretization method subject to boundary conditions, leads to an n-dimensional system of difference equations in the form of (6),

$\begin{matrix} {\left. \begin{matrix} {{x_{k + 1} = {{{H\left( v_{k} \right)}x_{k}} + {Bq}_{k}}},} \\ {{p_{k} = {{Mx}_{k} + D}},} \\ {{y_{k} = {Cp}_{k}},} \end{matrix} \right\} \text{:}\mspace{14mu} {G_{full}^{n}.}} & (6) \end{matrix}$

x_(k)≡[ x _(r)(s₁,t_(k)), . . . , x _(r)(s_(n),t_(k))]εR^(n) is the state of the system with entries equal to the average volume of cuttings in each discretized cell, p_(k)εR^(n) includes the pressure values at each cell along the annulus and y_(k)εR^(n) ^(y) includes the pressures at each sensor location. Similarly v_(k)≡[ ν _(r)(s₁,t_(k)), . . . , ν _(r)(s_(n),t_(k))]εR^(n) includes the uncertain average cuttings velocities in each cell which depends, for example, on mud velocity ν_(m) and the slip velocity of cuttings with respect to mud. Matrices H, MεR^(n−n), and B, DεR^(n) are results of the discretization scheme and are large and sparse. Matrix CεR^(n) ^(y) ^(×n), where n_(y)<<n, is simply a linear operator that selects pressures at the sensor locations.

Cuttings transport depends on the slip velocity between cuttings and mud. The slip velocity is the underlying uncertain parameter, which depends on cuttings size, shape and other factors. It can be assumed however that the variations of slip velocity are smooth along the annulus and changes in the velocity field at nearby time instances do not vary significantly. We examine the case where the uncertain velocity field ν₀ is a stationary Gaussian process ν₀˜N (μ_(ν), K_(ν)) with mean μ_(ν)=0.5 [m/sec] and covariance matrix K_(ν) with entries

${K_{i,j} = {\beta \; {\exp \left( {- \frac{{{s_{i} - s_{j}}}^{2}}{2\gamma^{2}}} \right)}}},\mspace{14mu} i,{j = 1},\ldots \mspace{14mu},n,$

correlation length γ=0.2L, L=200 meters and scale β=0.025.

First considered is the accuracy of the surrogate models in terms of the relative prior-weighted L² error, defined as

$\begin{matrix} {{e_{x}:=\frac{\int_{\Theta}{\sum\limits_{k = 0}^{N_{k} - 1}\; {{{{x_{k}(\theta)} - {{\hat{x}}_{k}(\theta)}}}_{2}{\pi_{pr}(\theta)}\ {\theta}}}}{\int_{\Theta}^{\;}{\sum\limits_{k = 0}^{N_{k} - 1}\; {{{x_{k}(\theta)}}_{2}\ {\pi_{pr}(\theta)}{\theta}}}}},} & (7) \end{matrix}$

where we use the notation x(θ) and {circumflex over (x)}(θ) to indicate the generation of the state (cuttings volume) and its approximation given a parameter value θ. Similarly e_(p) is defined as the relative prior-weighted error of the pressure along the annulus.

FIG. 12 shows error norms for cutting volume and pressure resulting from the approximate forward models versus the dimensionality of the surrogate model, in accordance with this example. Specifically, shown is the L² error in approximating the full forward model G_(full) of state dimensionality n=400, with a projection-based surrogate model G_(rom) ^(m). The error is decreased exponentially with increased order of approximation, where the term order in the case of projection-based approximation is defined as the number of basis modes in Φ. In this example, a naïve reduction in the parameter and state spaces has been performed, in the sense that no optimization techniques have been applied to construct (sub)-optimal models.

However, even this naïve dimensionality reduction can provide accurate approximations. FIG. 13 shows cuttings volume along the annulus at an instance in time obtained from the full model and its approximations, in accordance with this example. G_(full) is the full model of state and parameter dimensionality 400, G_(rom) ^(m) is the surrogate model of dimensionality m obtained from a reduction in the parameter space via Karhunen Loève expansion and state space reduction via proper orthogonal decomposition, and Ĝ_(rom) ^(m,d) is the surrogate model G_(rom) ^(m) with approximated nonlinearities via generalized polynomial chaos expansions of polynomial degree. As shown, the surrogate models yield highly accurate depth-sensitive estimates of cuttings volume. Thus, the use of improvement and/or optimization techniques to design surrogate models specifically for applications of interest (e.g., cuttings transport and gas migration) can provide improved approximations and lower dimensionalities.

The computational complexity of particle filtering can be reduced by considering a time evolution of M<N low dimensional particles {{circumflex over (μ)}_(k) ^((i))}_(i=1) ^(M)={{circumflex over (x)}_(k) ^((i)),{circumflex over (z)}_(k) ^((i))}_(i=1) ^(M) via Eqn. (3) and an update conditioned on real-time measurements according to the low dimensional probability density,

π({circumflex over (x)} _(k+1) ,{circumflex over (z)} _(k+1)|data).  (8)

In this example, actual values of densities, wellbore length etc. have not been used. This is done without any loss of generality, simply for the purpose of generating results that can be clearly visualized and assessed. To demonstrate results, considered are zero initial state conditions and the outputs of interest y_(k) ^(obs)εR^(n) ^(y) are observed at time intervals t_(k)ε[0,T] at n_(o)=3 sensors and the overall simulation time is T=900 seconds. Sensors were placed along the wellbore annulus at depths 0.25L, 0.5L and 0.75L meters from the bottom of the well. Simulations were considered for an annulus length L=200 meters, however the results hold for any arbitrary length. The measurements were obtained by perturbing the full model outputs with Gaussian noise. Also, in this example cuttings and mud densities are set to ρ_(r)=4 [kg/m³] and ρ_(m)=0.2[kg/m³]) and the bit diameter is D_(bit)=0.2 [m].

Table I shows results obtained by the solution to the inverse problem by using the full n-dimensional model, G_(full) ^(n) its approximation model using gPC, G_(full) ^(n,d), the POD model G_(rom) ^(m) and the gPC-POD model Ĝ_(rom) ^(m,d), of order m and polynomial degree d. More specifically the relative square errors (average error in time and space) are compared between the ‘true’ values of the state, pressure, output and slip velocity to their estimates obtained by solving the inverse problem using the full model and the approximation models. The average relative error norm of the state x and its mean estimate μ_(x), are defined as

$\begin{matrix} {E_{x}:={\frac{\sum\limits_{k = 0}^{N_{k} - 1}\; {{x_{k} - \mu_{x_{k}}}}_{2}^{2}}{\sum\limits_{k = 0}^{N_{k} - 1}\; {x_{k}}_{2}^{2}}.}} & (9) \end{matrix}$

TABLE I COMPARISON OF ESTIMATION RESULTS USING FULL AND APPROXIMATION MODELS; t_(sim) IS THE SIMULATION TIME REQUIRED FOR THE COMPLETION OF THE ESTIMATION. ERROR TERMS DEFINED IN (9). Ĝ_(full) ^(n, d) Ĝ_(rom) ^(m, d) G_(full) ^(n) n = 400, G_(rom) ^(m) m = 59, Model n = 400 d = 2 m = 20 m = 59 d = 2 t_(sim)[sec] 120 78.7 83.7 93.0 39.5 E_(x) 7.88e−003 6.00e−003 3.43e−002 6.82e−003 5.10e−003 E_(y) 6.02e−006 6.93e−006 2.37e−005 6.86e−006 6.74e−006 E_(p) 6.93e−005 4.45e−005 3.66e−004 5.47e−005 3.17e−005 E_(v) 3.05e−002 2.40e−002 6.63e−002 3.36e−002 2.91e−002

The errors E_(P), E_(y) and E_(v) are defined similarly for pressure, output and slip velocity. The results shown are not average results of many solutions to the inverse problem, however they are very similar in all the tested cases. The surrogate models provide comparable results provided the forward model approximation is accurate. Computational speed ups of 34.4% were obtained by approximating the nonlinearities of the full model directly with a model G_(full) ^(n,d=2) of full order n=400 and polynomial degree d=2, whereas computational speed ups of 30.2-38.5% were obtained by approximating the full model with a POD model G_(rom) ^(m) of order m=20 to m=59. Approximating the full model with a gPC-POD model Ĝ_(rom) ^(m,d) provided computational speed ups of 67.1%.

FIG. 14 shows estimates of pressure, cuttings volume and cuttings slip velocity along the annulus at instances in time, by incorporating a surrogate model in the particle filtering framework, in accordance with this example. Estimations were performed using the surrogate model Ĝ_(rom) ^(m=59,d=2) of dimensionality m=59 (for state and parameter spaces) and polynomial degree d=2 (for nonlinearities). Blue lines represent ‘true’ quantities, solid-red lines are mean estimations and dash-red lines are 2σ-error intervals. In this specific example, the surrogate model considers reduction in parameter and state spaces and approximation of nonlinearities, and the use of the surrogate model accelerated the particle filtering process by 67%.

FIG. 15 shows error bars representing the average L₂ norms for the mean error and standard deviations of the estimations from ‘true’ quantities of annulus pressure, sensor output pressure, cuttings volume and slip velocity, in accordance with this example. Estimations were performed using the full model G_(a)=G_(full) ^(n=400) and approximation models G_(b)=Ĝ_(full) ^(n=400,d=2), G_(c)=G_(rom) ^(m=20), G_(d)=G_(rom) ^(m=59) and G_(e)=Ĝ_(rom) ^(m=59,d=2). Remark :G_(full) is the full model of state and parameter dimensionality 400, Ĝ_(full) ^(d) is the full model with approximated nonlinearities via generalized polynomial chaos expansions of polynomial degree d, G_(rom) ^(m) is the surrogate model of dimensionality m obtained from a reduction in the parameter space via Karhunen Loève expansion and state space reduction via proper orthogonal decomposition, and G_(rom) ^(m,d) is the surrogate model G_(rom) ^(m) with approximated nonlinearities via generalized polynomial chaos expansions of polynomial degree d. As shown, comparable estimations are provided by the surrogate models and the full-scale model.

Example 3 Particle Filtering with Switching Models

FIG. 16 illustrates an example of a particle-filtering framework with switching models. The outputs of M evolution models at time t_(k) are denoted by {μ_(k) ^((i,n))}_(i=1) ^(N) ^(n) for n=1, . . . , M where M is the number of different models. The outputs of L observation models are denoted by {y_(k) ^((i,n))}_(i=1) ^(K) ^(n) for n=1, . . . , L. At time t_(k), each model outputs N, particles denoted by {μ_(k) ^((i,n))}_(i=1) ^(N) ^(n) for n=1, . . . , M. Each of these models could describe different behaviors of the process (e.g., normal operation, kick event, etc.). The process outputs {y_(k) ^((i,n))}_(i=1) ^(K) ^(n) for n=1, . . . , L can be obtained based on L different observation models, given the particles {μ_(k) ^((i,n))}_(i=1) ¹, . . . , {μ_(k) ^((i,n))}_(i=1) ^(M). These observation models could consider different states of sensors (e.g., working properly, complete failure, working with a bias error). At an instance in time, a number of particles will be generated based on the suitability of each model, which could allow monitoring the drilling process in the case of abrupt changes of its behavior.

In one embodiment of the present invention, data from the sensors is analyzed using a changepoint detection method. Changepoint detection methods are described in U.S. patent application Ser. No. 13/062,782, filed on Oct. 14, 2008 and entitled “SYSTEM AND METHOD FOR REAL-TIME MANAGEMENT OF AN AUTOMATED INDUSTRIAL PROCEDURE USING ONLINE DATA FUSION,” and published as PCT Publication No. WO 2010/043951. This reference is hereby incorporated by reference in its entirety for all. In a changepoint system, data is received from one or more of the sensors. Upon receiving a new data item from the input data stream from the sensor, the changepoint system:

-   -   postulates that the data stream is segmented according to a         plurality of possible segmentations each comprising a plurality         of segments divided by changepoints each changepoint indicative         of a change in operating condition; and     -   evaluates each segmentation by: fitting the input stream data         corresponding to each segment in the segmentation to a model         corresponding to the each segment in the segmentation; and         evaluating the segmentations by determining how well the models         for the segments of each segmentation fit the input data         corresponding to each segment of each segmentation. In this way,         the changepoint system segments the data stream. In an         embodiment of the present invention, the segmented data may be         used with the surrogate models.

Specific details are given in the above description to provide a thorough understanding of the embodiments. However, it is understood that the embodiments may be practiced without these specific details. For example, circuits may be shown in block diagrams in order not to obscure the embodiments in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments. Further, while the disclosure may reference, e.g., geophysical models or geophysical variables, it is understood that other embodiments may instead pertain to different contexts. For example, “geophysical” models, variables, etc. may relate to resource-drilling (e.g., oil drilling) operations, characterizations of underground features (e.g., cutting movement, gas migration, etc.), formations, etc. In some instances, the disclosure may pertain to non-geophysical applications.

Implementation of the techniques, blocks, steps and means described above may be done in various ways. For example, these techniques, blocks, steps and means may be implemented in hardware, software, or a combination thereof. For a hardware implementation, the processing units may be implemented within one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, micro-controllers, microprocessors, other electronic units designed to perform the functions described above, and/or a combination thereof.

Also, it is noted that the embodiments may be described as a process which is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process is terminated when its operations are completed, but could have additional steps not included in the figure. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, its termination corresponds to a return of the function to the calling function or the main function.

Furthermore, embodiments may be implemented by hardware, software, scripting languages, firmware, middleware, microcode, hardware description languages, and/or any combination thereof. When implemented in software, firmware, middleware, scripting language, and/or microcode, the program code or code segments to perform the necessary tasks may be stored in a machine readable medium such as a storage medium. A code segment or machine-executable instruction may represent a procedure, a function, a subprogram, a program, a routine, a subroutine, a module, a software package, a script, a class, or any combination of instructions, data structures, and/or program statements. A code segment may be coupled to another code segment or a hardware circuit by passing and/or receiving information, data, arguments, parameters, and/or memory contents. Information, arguments, parameters, data, etc. may be passed, forwarded, or transmitted via any suitable means including memory sharing, message passing, token passing, network transmission, etc.

For a firmware and/or software implementation, the methodologies may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. Any machine-readable medium tangibly embodying instructions may be used in implementing the methodologies described herein. For example, software codes may be stored in a memory. Memory may be implemented within the processor or external to the processor. As used herein the term “memory” refers to any type of long term, short term, volatile, nonvolatile, or other storage medium and is not to be limited to any particular type of memory or number of memories, or type of media upon which memory is stored.

Moreover, as disclosed herein, the term “storage medium” may represent one or more memories for storing data, including read only memory (ROM), random access memory (RAM), magnetic RAM, core memory, magnetic disk storage mediums, optical storage mediums, flash memory devices and/or other machine readable mediums for storing information. The term “machine-readable medium” includes, but is not limited to portable or fixed storage devices, optical storage devices, wireless channels, and/or various other storage mediums capable of storing that contain or carry instruction(s) and/or data.

While the principles of the disclosure have been described above in connection with specific apparatuses and methods, it is to be clearly understood that this description is made only by way of example and not as limitation on the scope of the disclosure. 

What is claimed is:
 1. A system for assessing operations at a resource drill site, the system comprising: an input receiver that receives inputs in real-time or near real-time from a plurality of sensors, wherein the plurality of sensors are located in a borehole penetrating an earth formation and the plurality of sensors comprise a first sensor located at a first depth respective to a ground level and a second sensor located at a second depth respective to the ground level, the first depth being different from the second depth; an estimator that estimates a value for each variable of one or more variables related to a geophysical characteristic associated with the resource drill site, the estimation being based on the inputs received by the input receiver, wherein the estimator applies one or more geophysical models to determine the estimated value for each variable of the one or more variables related to the geophysical characteristic; and a real-time estimate output that outputs the value for each variable of the one or more variables related to the geophysical characteristic in real-time or in near real-time.
 2. The system for assessing operations at the resource drill site as recited in claim 1, further comprising a geophysical model generator that generates the one or more geophysical models by reducing a dimensionality one or more corresponding full-scale models.
 3. The system for assessing operations at the resource drill site as recited in claim 1, wherein the one or more geophysical models comprise one or more models for cutting transport and/or gas migration.
 4. The system for assessing operations at the resource drill site as recited in claim 1, wherein the plurality of sensors are located along a wired drill string.
 5. The system for assessing operations at the resource drill site as recited in claim 1, the system further comprising: a predictor that predicts additional inputs from the plurality of sensors based on the one or more geophysical models; an analyzer that compares the predicted additional inputs to corresponding received inputs; and a model adjustor that adjusts the one or more geophysical models based on the comparison.
 6. The system for assessing operations at the resource drill site as recited in claim 1, the system further comprising: a space definer that defines one or more spaces representing potential values for one or more unknown variables in the one or more geophysical models; a particle sample that generates a plurality of particles, each particle being associated with a value for each unknown variable of the one or more unknown variables, the value for each unknown variable of the one or more unknown variables being based on a sampling from the defined one or more spaces; a model output analyzer that analyzes application of the model for each particle of the plurality of particles; and a particle weight assigner that assigns a weight to each particle of the plurality of particles based on the analysis performed by the model output analyzer.
 7. The system for assessing operations at the resource drill site as recited in claim 1, wherein the one or more geophysical models comprise a plurality of geophysical models, each geophysical model representing a different operational state associated with the resource drill site.
 8. The system for assessing operations at the resource drill site as recited in claim 1, wherein the one or more geophysical models comprise a plurality of geophysical models, wherein a first geophysical model assumes a reliable operation of each sensor of the plurality of sensors, and wherein the second geophysical model assumes that at least one sensor of the plurality of sensors is not reliably operating.
 9. A method for assessing operations at a resource drill site, the method comprising: receiving inputs in real-time or near real-time from a plurality of sensors, wherein the plurality of sensors are located along a borehole penetrating the earth and the plurality of sensors comprise a first sensor located at a first depth respective to a ground level and a second sensor located at a second depth respective to the ground level, the first depth being different from the second depth; estimating a value for each variable of one or more variables related to a geophysical characteristic associated with the resource drill site, the estimation being based on the inputs, wherein the value for each variable of the one or more variables related to the geophysical characteristic are estimated, at least in part, by applying one or more geophysical models; and outputting the value for each variable of the one or more variables related to the geophysical characteristic in real-time or in near real-time.
 10. The method for assessing operations at the resource drill site as recited in claim 9, the method further comprising generating the one or more geophysical models by reducing a dimensionality of one or more corresponding full-scale models.
 11. The method for assessing operations at the resource drill site as recited in claim 9, wherein the one or more geophysical models comprise one or more models for cutting transport and/or gas migration.
 12. The method for assessing operations at the resource drill site as recited in claim 9, wherein the plurality of sensors are located along a wired drill string.
 13. The method for assessing operations at the resource drill site as recited in claim 9, the method further comprising: predicting additional inputs from the plurality of sensors based on the one or more geophysical models; comparing the predicted additional inputs to corresponding received inputs; and adjusting the one or more geophysical models based on the comparison.
 14. The method for assessing operations at the resource drill site as recited in claim 9, the method further comprising: defining one or more spaces representing potential values for one or more unknown variables in the one or more geophysical models; generating a plurality of particles, each particle being associated with a value for each unknown variable of the one or more unknown variables, the value for each unknown variable of the one or more unknown variables being based on a sampling from the defined one or more spaces; analyzing an application of the model for each particle of the plurality of particles; and assigning a weight to each particle of the plurality of particles based on the analysis performed by the model output analyzer.
 15. The method for assessing operations at the resource drill site as recited in claim 9, wherein the one or more geophysical models comprise a plurality of geophysical models, each geophysical model representing a different operational state associated with the resource drill site.
 16. The method for assessing operations at the resource drill site as recited in claim 9, wherein the one or more geophysical models comprise a plurality of geophysical models, wherein a first geophysical model assumes a reliable operation of each sensor of the plurality of sensors, and wherein the second geophysical model assumes that at least one sensor of the plurality of sensors is not reliably operating. 